Groups in Which Commutativity Is a Transitive Relation

A group G is called a CT-group if commutativity is a transitive relation on the set of non-identity elements of G. This dissertation is concerned with the class of CT-groups. Finite and locally finite CT-groups are studied in detail with structure theorems given in both solvable and insolvable cases. The investigation of solvable CT-groups leads naturally to the study of fixed-point-free groups of automorphisms of abelian groups. Topics include a rank condition for the existence of fixed-point-free groups of automorphisms of abelian torsion groups, and the extensions of abelian groups by locally finite groups with fixed-point-free actions. Torsion-free solvable CT-groups and polycyclic CT-groups are also examined in detail with constructions and structure theorems. An additional topic studied is the subclass of groups in which all quotients of subgroups are CT.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Wu, Yu-Fen

Contributors dc:contributor

• Derek J.S.Robinson

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9904628

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86964